基于压缩感知的菲涅尔孔径编码无透镜成像(特邀)

Fresnel Zone Aperture Lensless Imaging by Compressive Sensing(Invited)

为了降低菲涅尔孔径编码成像的传输带宽,改善小尺寸像感器拼接成像质量,提出菲涅尔孔径编码成像的压缩感知重建算法。基于压缩感知理论框架对部分采样的编码图像重建可行性进行分析,指出压缩感知重建误差随波带片常数缩小而降低。根据重建图像中孪生像和原始像在梯度域稀疏性的差异,引入全变差正则化实现抑制孪生像的效果。建立压缩感知理论框架下图像重建目标函数,利用交替方向乘子法进行求解。结合编码图像的能量分布和采样模式的可实现性,测试了矩形采样和辐射线采样两种模式,对不同采样数据量下重建图像质量进行分析。结果表明,辐射线采样模式相比矩形采样模式具有更高的图像采样效率,且仅通过7.3%的实验测量数据就可以获得质量良好的图像,为多块小尺寸像感器拼接成像提供了理论基础,有利于拓展编码掩膜无透镜成像的应用领域。

The Fresnel Zone Aperture(FZA)lensless imaging utilizes a Fresnel zone plate to encode the incident light as a holographic pattern. The image could be reconstructed by using holographic imaging methods. Compared with other mask-based lensless imaging methods,FZA imaging does not need any calibration. However,the inherent twin-image effect in in-line holography degrades the reconstructed image quality. In addition,the frequency of recorded fringes becomes higher with the increase of the FZA radius. Thus,a large size of the sensor could record fine fringes and obtain a high-resolution image.Because of the expensive cost of a large-size sensor,using several separate small-size sensors instead of a large-size sensor is an alternate scheme to realize high-resolution imaging. Since only partial measurements could be obtained by multiple sensors,the compressive sensing technique should be utilized for image reconstruction. The restricted isometry property is the sufficient condition of compressive sensing,unfortunately, this property is difficult to verify for a given matrix. Since the Gaussian random measurement matrix is proved to be a universal compressive sensing matrix,it is used as a reference to test the signal recovery ability of the FZA sensing matrix. The results show the reconstruction error decreases with the shrinking of the FZA constant. When the FZA constant is equal to 0.5 mm,the reconstruction performance is almost consistent with the Gaussian random matrix. Thus,compressive reconstruction for FZA imaging is feasible. Since the twin image,the original image and the sum of the two satisfy the forward model,image reconstruction belongs to an ill-posed problem because of multiple solutions. The regularization method is necessary to keep the solutions unique and stable. According to the sparsity difference between the twin image and the original image in the gradient domain,Total Variation(TV)regularization is introduced to suppress the twin image. The objective function of image reconstruction consists of an error term evaluated on sampling area and a TV regularization term. In particular,the error term calculates the first-order difference of the residual between prediction and measurements,and it can effectively eliminate the interference of the constant term in the coded image and improve the image quality.The objective function is solved by the Alternating Direction Multiplier Method(ADMM). ADMM decomposes the complex problem into several subproblems which are easy to solve,and reduce the scale of the problem and the difficulty of solving. In simulation test,the sizes of the original image and coded image both are 256×256 pixels,and the pixel pitch is 10 μm. In combination with the energy distribution of the coded image and the realizability of sampling mode,rectangle sampling and radiation sampling are tested,and the quality of the reconstructed image under different sampling ratios are analyzed. Since the image sensor is not sensitive to oblique incident light,the actual field of view is limited to a small range,and the light intensity received by each pixel of the image sensor only comes from the superposition of the local small area corresponding to the projection of the FZA. The coded image presents a frequency distribution similar to that of the FZA,that is the frequency increases gradually from the center of the image to the edge. Since the spectral energy of most natural images is concentrated at low frequencies,the center of the image should be more densely sampled than the edges to match the energy distribution. The results show that the radiation sampling mode has higher image sampling efficiency than the rectangular sampling mode,and only 7.3% of the experimental measurement data can obtain good quality images. The proposed method provides a theoretical basis for the stitching imaging of multiple small image sensors,which is beneficial to expanding the application field of lensless imaging with a coded mask.